1. Field of Invention
The present invention relates to radio engineering. More particularly, the present invention relates to a method for signal transmission-reception in a multi-user multiple transmit and multiple receive antenna radio communication system.
2. Description of Related Art
The technology using multiple transmit and multiple receive antennas is attractive as an efficient method for improving communication channel throughput without requiring additional radio spectrum expense. In radio communication systems that apply the technology, a communication channel between transmit and receive sides has multiple inputs, transmit antennas, and multiple outputs, receive antennas. Hereupon the technology is called Multiple-Input-Multiple-Output (MIMO).
The entire set of signal propagation channels between transmit and receive antennas is called a MIMO channel. One method to increase throughput is the simultaneous transmission of different information flows over different spatial subchannels of the MIMO channel. This method is known as spatial multiplexing, examples of which are illustrated by G. J. Foshini, G. D. Golden, and R. A. Valenzuela, in “Simplified processing for high spectral efficiency wireless communication employing multi-element arrays,” IEEE Selected Areas Communication, vol. 17, pp. 1841-1852, November, 1999, and in the Institute of Electrical and Electronics Engineers (IEEE) 802.16™ Standard for local and metropolitan area networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems, 1 Oct. 2004.
According to the spatial multiplexing technique, independent information flows are transmitted via different transmit antennas. At the receive side the transmission coefficients hj,i of all spatial channels are estimated, where i, j are indices of the transmit and receive antennas forming the respective spatial channel. The channel matrix H is formed from the said coefficients and used at signal reception.
Until recently, transmit-receive methods for single-user MIMO channels with one receiver and one transmitter (point-to-point) have been widely developed.
An obstacle for MIMO technology application in the point-to-point system is the necessity to mount multiple antennas on the Subscriber Station (SS). This difficulty arises because the SS must generally meet small-size and low cost requirements.
Another problem of the single user MIMO technology is that the throughput increase depends on scattering properties of the signal propagation environment. In this case, to obtain a noticeable throughput gain, the signal propagation environment is required to have scattering objects and antenna systems to have antennas spaced a long distance from each other.
One method to address the problem is by means of the multi-user MIMO technology. According to this technology, a channel formed by multiple antennas of a Base Station (BS) on the one side and antennas of multiple SSs on the other is considered as a MIMO channel. Each SS may have a small number of antennas or even only one antenna as well.
Multi-user approaches make it possible to exploit additional advantages of the MIMO technology.
First, there is a possibility to increase throughput by spatial division when several subscriber stations use one and the same physical channel to communicate with the BS.
Second, a multi-user MIMO channel has relatively low correlation between spatial subchannels because they belong to different subscriber terminals. This provides throughput gain even in a low scattering environment.
Third, there is a possibility to implement MIMO algorithms when a subscriber station has one antenna or a small number of antennas.
At present, there is known an efficient solution for the multi-user MIMO algorithm in the uplink (from SSs to the BS). The solution includes a method of collaborative spatial multiplexing used to transmit signals from multiple SSs to a BS. This solution is taken into account by modern communication standards such as the IEEE 802.16™ Standard for local and metropolitan area networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems, 1 Oct. 2004.
However, the problem of increasing capacity is more important for the downlink (from the BS to SSs) over which greater volume and high-rate data flows are transmitted. At the same time, there is no simple and efficient multi-user algorithm for a MIMO downlink Implementation of multi-user MIMO approaches in the downlink faces two major problems. The first problem is the need to provide the transmitter with communication channel information. The second problem is that joint processing of signals of different subscriber terminals is virtually impossible in the multi-user channel in contrast to the single-user MIMO channel.
Therefore, development of a multi-user MIMO algorithm of signal transmission-reception in the communication system downlink is a relevant and important task.
Downlink multi-user technology generally consists in signal transformation before its on-air transmission, whereby transformation is usually called pre-transmission or precoding. There are several multi-user MIMO approaches known in the downlink. The different approaches include dirty paper coding as illustrated by M. Airy, A. Forenza, R. W. Heath, Jr., and S. Shakkottai, in “Practical Costa precoding for the multiple antenna broadcast channel,” IEEE Global Telecommunications Conference, GLOBECOM, 29 Nov.-3 Dec. 2004, Volume 6, Page(s): 3942-3946, block diagonalization as illustrated by Q. H. Spencer, and M. Haardt, in “Capacity and Downlink Transmission Algorithms for a Multi-user MIMO Channel,” Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference, Volume 2, Issue, 3-6 Nov. 2002 Page(s): 1384-1388, and various methods of linear multi-user precoding such as illustrated by J. C. Mundarath, and J. H. Kotecha, in “Zero-Forcing Beamforming for Non-Collaborative Space Division Multiple Access,” Proceedings of 2006 IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP, 14-19 May 2006, Volume: 4, page(s): IV-IV, and A Wiesel, Y. C. Eldar, and Sh. Shamai, in “Optimal Generalized Inverses for Zero Forcing Precoding,” 41st Annual Conference on Information Sciences and Systems, CISS '07, 14-16 Mar. 2007, pages: 130-134.
However, most of the methods are of high implementation complexity and require complex study before their practical use.
For example, a block diagonalization algorithm that is a theoretically efficient implementation method for multi-user MIMO technology is illustrated by Q. H. Spencer, and M. Haardt, in “Capacity and Downlink Transmission Algorithms for a Multi-user MIMO Channel,” Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference, Volume 2, Issue 3-6, Nov. 2002, Page(s): 1384-1388. According to this algorithm, multi-user signal precoding is performed in such a way that the MIMO channel is transformed into orthogonal spatial sub-channels corresponding to different subscriber terminals. These channels do not generate mutual interference. Signal transmission-reception of each subscriber terminal is executed in the respective spatial sub-channel using one of the known signal-user MIMO algorithms.
To implement the above approach it is necessary to estimate transmission coefficients of all spatial communication channels and to form a channel matrix. Channel matrix information includes auxiliary control information and shall be transmitted to the BS in any manner. The BS shall then make a singular value decomposition of the channel matrix. The BS uses the resulting information about right singular vectors during signal transmission. Information about left singular vectors shall be transmitted from the BS to SSs so that they will be able to receive a signal.
Implementation of this algorithm is complex as it requires two-way, high rate transmission of high volume control data. Another disadvantage of the algorithm is that it is applicable only in the case when subscriber terminals have two or more receive antennas.
Other and more simple linear multi-user precoding methods are known including Minimum Mean Squared Error (MMSE) and Zero Forcing (ZF) methods as illustrated by [J. C. Mundarath, and J. H. Kotecha, in “Zero-Forcing Beamforming for Non-Collaborative Space Division Multiple Access,” Proceedings of 2006 IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP, 14-19 May 2006, Volume: 4, page(s): IV-IV, and by A. Wiesel, Y. C. Eldar, and Sh. Shamai, in “Optimal Generalized Inverses for Zero Forcing Precoding,” 41st Annual Conference on Information Sciences and Systems, CISS '07, 14-16 Mar. 2007, pages: 130-134.
According to these algorithms, signal precoding is executed by a linear transformation whose matrix is formed by inversion or pseudo-inversion of the channel matrix H. As a result of precoding, only the desired signal is generated in each receive antenna of each of SS with no interference created by signals intended for other receive antennas. The ZF and MMSE methods are applicable for terminals equipped by one antenna and multiple antennas as well.
One of the simplest multi-user precoding methods is a method of channel inversion or ZF.
According to the channel inversion method, the packet a1, . . . , aS is formed from modulation symbols to be simultaneously transmitted to U SSs, where S is the summed number of the SS receive antennas and the number of symbols transmitted to each SS equals the number of receive antennas of the given SS.
A packet is represented as the vector a=[a1 . . . aS]T, whose elements (or coordinates) are packet symbols.
The transmitted signal vector s is formed from the given vector by multiplying the vector a by the channel matrix inversion or pseudo-inversion if the matrix H is not square. For simplicity, consider the case of S=N when the matrix H is square. Then,s=H−1a  (1)
A multitude of signals received by an SS can be represented as elements of the vector which in turn could be expressed asy=Hx+n,  (2)where n is a vector of receive antenna noise components which are well approximated as independent Gaussian random values, and x is a normalized transmitted signal vector obtained by transforming the vector s:
                              x          =                      s                                          E                ⁡                                  [                  γ                  ]                                                                    ,                            (        3        )            γ=∥s∥2 is signal power and, E[γ] is mathematical expectation of γ.
By substituting (1) and (3) into (2), one can get
                              y          =                                                    1                                                      E                    ⁡                                          [                      γ                      ]                                                                                  ⁢                              I                s                            ⁢              a                        +            n                          ,                            (        4        )            
where n denotes a noise component vector of the SS receive antennas, and IS is a unitary diagonal matrix of S×S size.
It can be seen from (4) that the received signals of users are mutually independent and do not create mutual interference. However, normalization (3) leads to the signal transmission coefficient being equal to
      1                  E        ⁡                  [          γ          ]                      .The value of γ=∥s∥2=∥H−1a∥2 in the denominator of the expression depends on inversion of the channel matrix H and could be quite high especially in a poor conditioned channel. Presence of this coefficient is the main reason of reducing the relative useful power at the receive point and respective lowering of the reception interference stability.
Therefore, an increase of the signal power because of multi-user precoding is the major disadvantage of the ZF and MMSE methods. Since there is a transmission power limitation in a communication system, the signal amplitude is linearly decreased (according to (3)). However, it leads to great reduction of the desired signal power relative to noise at the receive point. As a result, the reception interference stability becomes low.
There is another method for transmission power limitation that avoids significant reduction of relative desired power at the receive point. The method is based on the non-linear modulo reducing operation (or modulo operation) used in signal pre-processing algorithms, such as illustrated by R. F. H. Fischer, C. Windpassinger, A. Lampe, and J. B. Huber, in “Space-Time Transmission using Tomlinson-Harashima Precoding,” In Proc. 4th Int. ITG Conf., pp. 139-147, Berlin, January 2002.
The modulo operation consists of adding to the real and imaginary parts of an input number the values which are multiple of the real value A called a modulo. An input value of the mentioned operation is a complex number representing a transformed signal. The added values are selected in such a way that the summed complex number is in the central domain of the complex plane where all complex symbols of the used constellation are located. Hence, the transmitted signal power is reduced. The modulo value is known at both the transmit and receive sides and thus allows recovery of the signal reduced during reception.
The most efficient way of using the non-linear modulo operation is a vector perturbation algorithm as illustrated by Christoph Windpassinger, Robert F. H. Fischer, and Johannes B. Huber, in “Lattice-Reduction-Aided Broadcast Precoding,” IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 12, DECEMBER 2004, pp. 2057-2060.
Vector perturbation includes adding a certain perturbing vector p to the information symbol vector a. The resulting signal after multi-user precoding can be represented asx=H−1(a+p)  (5)
Real and imaginary parts of elements of the vector p are determined to be multiple of modulo A selected so that
                                          -                          A              2                                <                      Re            ⁢                                                  ⁢            a                          ,                              Im            ⁢                                                  ⁢            a                    <                      A            2                          ,                            (        6        )            where Rea, Ima are real and imaginary parts of any complex symbol of the applied modulation constellation.
The signal y received in the channel of each receive antenna of each subscriber station is subject to non-linear modulo operation
                                          y            ~                    =                                    z              ~                        +                          j              ·                              c                ~                                                    ⁢                                  ⁢        where                            (        7        )                                                      z            ~                    =                      z            ⁢                                                  ⁢            mod            ⁢                                                  ⁢            A                          ,                              c            ~                    =                      c            ⁢                                                  ⁢            mod            ⁢                                                  ⁢            A                          ,                  z          =                      Re            ⁡                          (              y              )                                      ,                  c          =                      Im            ⁡                          (              y              )                                      ,                            (        8        )                                          x          ⁢                                          ⁢          mod          ⁢                                          ⁢          A                =                  x          -                      A            ·                          ⌊                                                x                  +                                      A                    /                    2                                                  A                            ⌋                                                          (        9        )            └x┘ is a maximum integer not exceeding x.
The main feature of the modulo operation is it is invariant to adding of-fold values:(y+rA)mod A=ymod A,  (10)
where r is any integer.
Owing to this feature, after modulo operation, signals of the receive antennas of all SS can be represented by the vector{tilde over (y)}[H·H−1·(a+p)+n]mod A=ISa+n  (11)
where IS is a unitary diagonal matrix of S×S size.
This equality proves that vectors of the transmitted and received signals are linearly connected by means of the diagonal matrix IS. That is, multi-user precoding results in forming the desired signal in each receive antenna with no interference generated by the signals transmitted for other receive antennas.
The maximum multi-user precoding efficiency is achieved when the power of the transmitted signal x=H−1·(a+p) is reduced as much as possible by selecting the perturbing vector p. That is, the optimal perturbing vector popt shall be determined in the transmitter such that its addition to the information symbol vector a provides the signal power minimum after multi-user precoding:
                                          p            opt                    =                      arg            ⁢                                                  ⁢                                          min                                  p                  ∈                                      A                    ⁢                                                                                  ⁢                                          •                      Z                      S                                                                                  ⁢                                                                                                            H                                              -                        1                                                              ⁡                                          (                                              a                        +                        p                                            )                                                                                        2                                                    ,                            (        12        )            where □sz is a set of S-dimensional vectors whose elements have integer-valued real and imaginary parts.
Resolving of optimization task (12) is complicated in that the set of integers is not constrained, hence the set □sz is infinite. Therefore, exhaustive search of all values of the set □sz is impossible. Although the set of the considered integers can be limited by some values close to zero, e.g., {−2, −1, 0, 1, 2}, even in this case the search set could be extensive. For example, if the search set is composed of (52)S=625 vectors at S=2 and (52)S=390625 vectors at S=4. Therefore, the exhaustive search method to resolve (12) leads to a substantial increase of implementation complexity.
One approach to resolving the optimization task (12) consists in the use of lattice basis reduction as illustrated by Christoph Windpassinger, Robert F. H. Fischer, and Johannes B. Huber, in “Lattice-Reduction-Aided Broadcast Precoding,” IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 12, DECEMBER 2004, pp. 2057-2060. This method consists of the following.
The method for signal transmission-reception in a radio communication system, containing a transmit station equipped with N transmit antennas and U receive stations, where U≧2, each receive station is equipped with at least one receive antenna, and the summed number of receive antennas of the receive stations S fulfills the condition 1<S≦N, consists of the following:                transmission coefficients of a set of spatial communication channels are estimated, each channel being formed by one transmit antenna of a transmit station and one receive antenna of a receive station,        signals are transmitted-received between the transmit and receive stations for which:        at the transmit station, U sets of modulation symbols are formed from U information messages to be transmitted to U receive stations,        packets of S modulation symbols each are formed from the formed sets of the modulation symbols by including in a packet one modulation symbol per each of the receive antennas of the receive stations,        a modulation symbol packet is presented in the form of a vector of transmitted modulation symbols a=[a1 . . . aS]T,        the channel matrix H is formed from the transmission coefficients of spatial communication channels,        a real-valued vector ar and a matrix Hr are formed from the vector of transmitted modulation symbols a and the channel matrix H by the equations:        
                                          a            r                    =                                                    [                                                                                                    Re                        ⁢                                                                                                  ⁢                        a                                                                                                                                                Im                        ⁢                                                                                                  ⁢                        a                                                                                            ]                            ⁢                                                          ⁢                              H                r                                      =                          [                                                                                          Re                      ⁢                                                                                          ⁢                      H                                                                                                                          -                        Im                                            ⁢                                                                                          ⁢                      H                                                                                                                                  Im                      ⁢                                                                                          ⁢                      H                                                                                                  Re                      ⁢                                                                                          ⁢                      H                                                                                  ]                                      ,                            (        13        )            where ReY and ImY are matrices composed of real and imaginary parts of the respective elements of the matrix Y,                the linear multi-user signal pre-transformation matrix Wr is formed from the real-valued channel matrix Hr,Wr=(HrHHr)−1HrH,  (14)        by reducing the lattice basis of the matrix Wr the integer-valued matrix T with a determinant equal to ±1 is formed in such a way that multiplication by this matrix transforms the multi-user linear pre-transformation matrix to the matrix Z=WrT with a low condition number,        using the matrix T a perturbing vector is determined by the formula:p0=−T·A·Q(T−1·ar/A),  (15)where Q(x) is a vector derived from the vector x by rounding its elements to the nearest integers,        A is a real number so that real Rea and imaginary Ima parts of any modulation symbol are strictly less than A/2 by the absolute value:        
                                          -                          A              2                                <                      Re            ⁢                                                  ⁢            a                          ,                              Im            ⁢                                                  ⁢            a                    <                      A            2                                              (        16        )                            a perturbed real-valued vector of transmitted modulation symbols is formed by summing the real-valued vector of transmitted modulation symbols and a perturbing vector and linear multi-user pre-transformation of the obtained perturbed real-valued vector of modulation symbols is performed, thus forming a real-valued vector of transmitted signals:xr=Wr(ar+p0),  (17)        a transmitted signal vector is formed from the obtained real-valued vector of transmitted signals xr:x=xr(1:N)+j·xr(N+1:2N),  (18)where j means an imaginary unit and xr(n:m) denotes a vector composed of a sequence of elements of the vector xr from the n-th to the m-th element,        a set of signals determined by elements of the transmitted signal vector x is transmitted over all transmit antennas, by one signal over an antenna,        signals are received at each of U receive stations, while reception is performed in a channel of each receive antenna and during reception,        a signal y is formed as a complex number with a modulo and an argument representing the signal amplitude and phase received by a channel of the given antenna, respectively,        real and imaginary parts of the signal are determined as:z=Rey, c=Imy  (19)        a modulo operation is executed over the obtained signals z and c with the modulo equal to A:        
                                          z            ~                    =                      z            -                          A              ⁢                              ⌊                                                      z                    +                                          A                      /                      2                                                        A                                ⌋                                                    ⁢                                  ⁢                                            c              ~                        =                          c              -                              A                ⁢                                  ⌊                                                            c                      +                                              A                        /                        2                                                              A                                    ⌋                                                              ,                                    (        20        )            where └x┘ is an integer part of x, (i.e., the maximum integer not exceeding x),                a complex signal {tilde over (y)}={tilde over (z)}+j{tilde over (c)} is formed from the signals {tilde over (z)} and {tilde over (c)} and using values of the complex signal {tilde over (y)} thus formed in a channel of each receive antenna, the received signal is demodulated and decoded.        
The method for signal transmission-reception in a multi-user MIMO communication system applies linear signal pre-transformation based on channel matrix inversion (or pseudo-inversion).
It is an efficient method for multi-user precoding for at least two reasons. First, mutual signal interference is suppressed in receive antennas as a result of this transformation. Second, the receive side does not require any additional auxiliary information for signal demodulation, thus making possible relatively simple implementation of the receive unit.
However, due to signal multiplication by channel matrix inversion (or pseudo-inversion) signal power is greatly increased. Vector perturbation is used to reduce power.
In this case an optimal perturbing vector is determined as a vector minimizing the value of ∥Wr·(p+ar)∥2.
The task of searching for an optimal perturbing vector could be represented as a task of searching for the vector Wr·p, which is maximally close to the vector −Wr·ar. In the matrix theory, a set of vectors Wr·p is known as a lattice space of the matrix Wr. A search within the lattice space is greatly simplified if a matrix has a low condition number, which is the ratio of the maximum singular value to the minimum one. In this case, the matrix has a greater degree of column orthogonality and the solution of Wr·p=−Wr·ar can be approximated as follows:
                              p          =                                    -              A                        ·                          Q              ⁡                              (                                                      a                    r                                    A                                )                                                    ,                            (        21        )            where Q(x) is rounding up of the vector x elements to the closest integers.
The approximation accuracy depends on the orthogonality degree of the matrix Wr columns or proximity of its condition number to one.
To reduce the condition number of matrix Wr, the lattice basis reduction method is used. In this case, the linear pre-transformation matrix Wr is transformed to the matrix Z with a low condition number and higher degree of column orthogonality. Lattice basis reduction consists in forming the integer-valued matrix T with a determinant of ±1 so that the equality Z=WrT is fulfilled between the source and transformed matrices.
After transformation, the optimum perturbing vector is found as follows:
                              p          0                =                              -            T                    ·          A          ·                      Q            ⁡                          (                                                                    T                                          -                      1                                                        ·                                      a                    r                                                  A                            )                                                          (        22        )            
However, in spite of the fact that the lattice basis reduction reduces in average the matrix condition number and increases its column orthogonality degree, it does not ensure ideal column orthogonality of the linear pre-transformation matrix. As a consequence, the selected perturbing vector does not always provide the minimum of ∥Wr·(p+ar)∥2. This produces an increase in the average transmitted signal power and an increase in the range of transmitted signal power values.
The first aspect leads to a decrease in the channel throughput due to a decrease of the desired signal power at the receive point caused by power normalization during transmission. The second aspect results in an increase in the peak-to-average power ratio. This in its turn increases requirements of the amplifier linearity and complicates implementation of the method in communication hardware.